A question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and decide the appropriate answer.
Question: Ax, Bk, Cq, Dp and Ev are sitting around a circular table, facing the centre. Who sits to the immediate left of Cq?
Statements:
(I) Bk sits second to the left of Ev. Dp sits second to the right of Ev.
(II) Ax sits second to the right of Cq. Dp sits to the immediate left of Bk.
Correct Answer :
Data in Statement II alone is sufficient to answer the question, while data in statement I is not.
Solution :
The correct option is: Data in Statement II alone is sufficient to answer the question, while data in statement I is not.
Let's analyze the question and the statements step-by-step to understand why Statement II alone is sufficient to answer the question, whereas Statement I alone is not.
We are given that five persons: Ax, Bk, Cq, Dp, and Ev are sitting around a circular table facing the centre. Facing the centre means that for any person, their right is in the counter-clockwise direction, and their left is in the clockwise direction.
Step 1: Analyze Statement (I) alone
Statement (I) states:
1. Bk sits second to the left of Ev.
2. Dp sits second to the right of Ev.
Let us place Ev at a position. Since Bk is second to the left of Ev, counting two positions clockwise from Ev gives the position of Bk. Since Dp is second to the right of Ev, counting two positions counter-clockwise from Ev gives the position of Dp.
So far, we have fixed the relative positions of Ev, Bk, and Dp. The remaining two positions must be occupied by Ax and Cq. However, Statement I does not provide any information about the relative positions of Ax and Cq. Thus, Cq could be sitting in either of the two remaining seats, and we cannot uniquely determine who sits to the immediate left of Cq.
Therefore, Statement I alone is NOT sufficient.
Step 2: Analyze Statement (II) alone
Statement (II) states:
1. Ax sits second to the right of Cq.
2. Dp sits to the immediate left of Bk.
Let us place Cq at a position. Since Ax sits second to the right of Cq, Ax is placed two positions counter-clockwise from Cq. This leaves three consecutive seats between Cq and Ax (going clockwise from Cq to Ax: Cq, seat 1, seat 2, seat 3, Ax).
Now we need to place Dp and Bk. We are told that Dp sits to the immediate left of Bk. This means Dp and Bk must sit next to each other, with Dp being clockwise next to Bk (since left is clockwise).
Let's look at the remaining vacant positions. We have 5 seats in total. Ax and Cq occupy two seats with one seat between them (going clockwise from Ax to Cq). The configuration of seats in clockwise order starting from Cq is:
Cq → Seat A → Ax → Seat B → Seat C → Cq
Here, Seat A is between Cq and Ax. Seat B and Seat C are between Ax and Cq.
Since Dp must sit to the immediate left of Bk (i.e., Bk → Dp in counter-clockwise order, or Dp → Bk in clockwise order), they must occupy two adjacent seats. The only adjacent empty seats available are Seat B and Seat C. Seat A is isolated between Cq and Ax.
Therefore, the adjacent seats (Seat B and Seat C) must be occupied by Dp and Bk. Specifically, going clockwise:
From Ax, we go to Seat B, then Seat C, then Cq.
Since Dp is to the immediate left of Bk, Dp must be clockwise from Bk. Thus, Bk must be at Seat B, and Dp must be at Seat C.
This leaves the remaining person, Ev, to occupy the single isolated Seat A between Cq and Ax.
So, the final clockwise arrangement of the five people is:
Cq → Ev → Ax → Bk → Dp → Cq
From this complete and unique arrangement, we can see that Ev sits to the immediate left (clockwise direction) of Cq.
Therefore, Statement II alone is sufficient to answer the question.
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